Let `a , b , c , d , e ,f in R` such that `a d+b e+cf=sqrt((a^2+b^2+c^2)(d^2+e^2+f^2))` Use vector to prove that `(a+b+c)/(sqrt(b^2+b^2+c^2))=(d+e+f)/(sqrt(d^2+e^2+f^2))`

If (a)/(b) = (c)/(d) , show that : (a + b) : (c + d) = sqrt(a^(2) + b^(2)) : sqrt(c^(2) + d^(2))

If a,b,c,d ,e are +ve real numbers such that a+b+c+d+e=8 and a^2 + b^2 +c^2 + d^2 +e^2 = 16 , then the range of 'e' is

if a : b = e : d , show that : 3a + 2b : 3a - 2b = 3c + 2d : 3c - 2d .

The A D ,B Ea n dC F are the medians of a c A B C , then (A D^2+B E^2+C F^2):(B C^2+C A^2+A B^2) is equal to

If a ,b ,c ,d ,e ,f are A.M.s between 2 and 12, then find the sum a+b+c+d+e+fdot

(a)/(b) = (c)/(d) = (e)/(f) = k(a, b, c, d, e, f gt 0) then (A) k = (a + c +e)/(b + d + f) (B) k = (a^(2) + c^(2) +e^(2))/(b^(2) + d^(2) + f^(2)) (C) k = (c^(2)e^(2))/(d^(2)f^(2)) (D) k = ((ace)/(bdf))^((1)/(3))

If a,b,c,d,e, f are A. M's between 2 and 12 , then find a + b + c +d + e +f.

if a,b,c,d,e and f are six real numbers such that a+b+c=d+e+f a^2+b^2+c^2=d^2+e^2+f^2 and a^3+b^3+c^3=d^3+e^3+f^3 , prove by mathematical induction that a^n+b^n+c^n=d^n+e^n+f^n forall n in N .

If AD, BE and CF are the medians of a DeltaA B C ,t h e n(A D^2+B E^2+C F^2):(B C^2+C A^2+A B^2) is equal to

If theta=3alpha and sintheta=a/(sqrt(a^2+b^2)), the value of the expression acos e calpha-bsecalpha is (a) a/(sqrt(a^2+b^2)) (b) 2sqrt(a^2+b^2) (c) a+b (d) none of these